The wigs or hairpieces comprise an internal support or cap shaped in order to cover the user's scalp and on which natural or artificial hair is affixed, where this internal support is equipped with mechanisms or constructed in order to allow the attachment of the wig onto the user's head.
The internal support or cap is generally comprised of different parts identified by the areas of the head that they are intended to cover, such as, for example:                a top piece designed to cover an area of the skull that goes from the frontal bone to the middle point;        a left side and a right side (including brackets)        a rear piece; and        a part designed to cover the nape of the neck.        
The wigs can be made according to different known processes. For example:                A) A process referred to as the “machine” process, according to which the bands or wefts of hair (hair sewn together by a braid made by the machine) are sewn together on cotton or elastic ribbons, mainly for the nape of the neck and the sides; the bands or the wefts can also be sewn together partially or totally onto a lightweight fabric made of a network of stitches such as tulle, notably for the top piece.        B) A process referred to as the “hand” process, according to which the hair is tied separately or in groups of two to four on a tulle or light fabric having similar stitches.        C) A process referred to as the “monofilament” process, according to which the hair is tied on a base of translucent material, in a manner so as to imitate the natural implantation of a scalp.        
It is understood that regardless of the manufacturing process, the internal support or cap of the wig must have a shape and dimensions that enable it to closely fit, as best possible, the shape of the skull of the person who must wear it.
In order to meet the above requirement, the wigs are mainly manufactured according to a standard size corresponding to the average in the market for these articles.
The contour of their cap is equipped with adjustable brackets that enable an adjustment on the order of +/−2 cm of this contour, which is of course, insufficient to cover all of the shapes of the head. A same wig model is then most often made in three different sizes for each one of the proposed colors, in order to best meet the demand, which does not solve, in a very satisfying manner, the problem posed by the particular shape of the each individual's skull, and has, in addition, the disadvantage of creating storage/stocking problems, and unfavorably affecting the cost of the articles.
The adjustable brackets are installed in the area of the nape of the neck of the cap of the wigs in order to reduce the contour of the wig. However, if these caps make it possible to obtain a reduction of the external circumference of the wig, only the base of the area of the nape of the neck is “correctable” and this correction can alter the curve of the wig (from temple to temple and/or from front to back).
It is possible, of course, to make, according to the different processes mentioned above, custom-tailored wigs (U.S. Pat. No. 5,133,370 A), but, in this case, the cost price of these articles is extremely high and the time necessary to make them is very long, of course.
In the document U.S. Pat. No. 4,016,888A, a solution has been proposed for solving the problem of the reduction of the size of a wig from the standard model in order to give it the characteristics of a small or an extra-small size, by a contraction of the cap on which the hair is implanted, a contraction obtained using three brackets for flexible attachment equipped with a connecting element that is able to be attached to one or the other of two complementary spaced out and fixed connection elements. These contraction mechanisms are affixed to the inside of the cap, in the median part of it, and they are placed in parallel along the contour lines going from the nape of the neck to the frontal area.
If it can be acknowledged that the process described in the above document makes it possible to reduce the size of a standard wig model, this method does not allow an adjustment of this wig to the user's head, the shape of which does not correspond to that of the “standard” head for which the wig has been made. In fact, the adjustment that such a system can allow only involves the contour of the front nape of the neck, which is not sufficient for allowing a satisfactory adjustment in the majority of the varied shapes of the head.
In addition, the contraction obtained by the device described in this document, between two attachment points, leads to the formation of a outside bulge going from one temple to the other, this unaesthetic bulge being more or less pronounced in going from the standard size to the small size to the extra-small size.
An object of the invention is to correct these disadvantages.